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Which ordered pairs are solutions to the inequality 2y−x≤−6 ?

Select each correct answer.



(0, −3)

(2, −2)

(1, −4)

(6, 1)

(−3, 0)

Respuesta :

redheadangel
try plugging them in, might seem tedious, but it's the best way to practice. if you plug in a pair and the left side of the equation is less than or equal to 6, it's the right answer.
calculista

we have

[tex]2y-x\leq -6[/tex]

we know that

if a ordered pair is a solution of the inequality

then

the ordered pair must satisfy the inequality

we will proceed to verify each case to determine the solution of the problem

case A) [tex](0,-3)[/tex]

Substitute the value of x and y in the inequality, if the inequality is true, then the ordered pair is a solution of the inequality

so

[tex]2*(-3)-0\leq -6[/tex]

[tex]-6\leq -6[/tex] -------> Is True

therefore

the ordered pair [tex](0,-3)[/tex] is a solution of the inequality

case B) [tex](2,-2)[/tex]

Substitute the value of x and y in the inequality, if the inequality is true, then the ordered pair is a solution of the inequality

so

[tex]2*(-2)-2\leq -6[/tex]

[tex]-6\leq -6[/tex] -------> Is True

therefore

the ordered pair  [tex](2,-2)[/tex] is a solution of the inequality

case C) [tex](1,-4)[/tex]

Substitute the value of x and y in the inequality, if the inequality is true, then the ordered pair is a solution of the inequality

so

[tex]2*(-4)-1\leq -6[/tex]

[tex]-9\leq -6[/tex] -------> Is True

therefore

the ordered pair  [tex](1,-4)[/tex] is a solution of the inequality

case D) [tex](6,1)[/tex]

Substitute the value of x and y in the inequality, if the inequality is true, then the ordered pair is a solution of the inequality

so

[tex]2*(1)-6\leq -6[/tex]

[tex]-4\leq -6[/tex] -------> Is False

therefore

the ordered pair  [tex](6,1)[/tex] is not a solution of the inequality

case E) [tex](-3,0)[/tex]

Substitute the value of x and y in the inequality, if the inequality is true, then the ordered pair is a solution of the inequality

so

[tex]2*(0)-(-3)\leq -6[/tex]

[tex]3\leq -6[/tex] -------> Is False

therefore

the ordered pair  [tex](-3,0)[/tex] is not a solution of the inequality

therefore

the answer is

[tex](0,-3)[/tex]

[tex](2,-2)[/tex]

[tex](1,-4)[/tex]

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